The Schröder-Hipparchus numbers give an interesting example:

According to a line in Plutarch's Table Talk, Hipparchus showed that the number of "affirmative compound propositions" that can be made from ten simple propositions is 103049 and that the number of negative compound propositions that can be made from ten simple propositions is 310952. This statement went unexplained until 1994, when David Hough, a graduate student at George Washington University, observed that there are 103049 ways of inserting parentheses into a sequence of ten items. A similar explanation can be provided for the other number: it is very close to the average of the tenth and eleventh Schröder–Hipparchus numbers, 310954, and counts bracketings of ten terms together with a negative particle

 

The problem of counting parenthesizations was introduced to modern mathematics by Schröder (1870).

If this interpretation is correct it's a non-trivial combinatorial problem that Hipparchus solved. Hipparchus must have known some combinatorial techniques that are not in any contemporary sources that survive today but which were rediscovered in the 19th century.

The Schröder-Hipparchus numbers give an interesting example:

According to a line in Plutarch's Table Talk, Hipparchus showed that the number of "affirmative compound propositions" that can be made from ten simple propositions is 103049 and that the number of negative compound propositions that can be made from ten simple propositions is 310952. This statement went unexplained until 1994, when David Hough, a graduate student at George Washington University, observed that there are 103049 ways of inserting parentheses into a sequence of ten items. A similar explanation can be provided for the other number: it is very close to the average of the tenth and eleventh Schröder–Hipparchus numbers, 310954, and counts bracketings of ten terms together with a negative particle

The problem of counting parenthesizations was introduced to modern mathematics by Schröder (1870).

If this interpretation is correct it's a non-trivial combinatorial problem that Hipparchus solved. Hipparchus must have known some combinatorial techniques that are not in any contemporary sources that survive today but which were rediscovered in the 19th century.

The Schröder-Hipparchus numbers give an interesting example:

According to a line in Plutarch's Table Talk, Hipparchus showed that the number of "affirmative compound propositions" that can be made from ten simple propositions is 103049 and that the number of negative compound propositions that can be made from ten simple propositions is 310952. This statement went unexplained until 1994, when David Hough, a graduate student at George Washington University, observed that there are 103049 ways of inserting parentheses into a sequence of ten items. A similar explanation can be provided for the other number: it is very close to the average of the tenth and eleventh Schröder–Hipparchus numbers, 310954, and counts bracketings of ten terms together with a negative particle

The problem of counting parenthesizations was introduced to modern mathematics by Schröder (1870).

If this interpretation is correct it's a non-trivial combinatorial problem. Hipparchus must have known some combinatorial techniques that are undocumented elsewhere.

The Schröder-Hipparchus numbers give an interesting example:

According to a line in Plutarch's Table Talk, Hipparchus showed that the number of "affirmative compound propositions" that can be made from ten simple propositions is 103049 and that the number of negative compound propositions that can be made from ten simple propositions is 310952. This statement went unexplained until 1994, when David Hough, a graduate student at George Washington University, observed that there are 103049 ways of inserting parentheses into a sequence of ten items. A similar explanation can be provided for the other number: it is very close to the average of the tenth and eleventh Schröder–Hipparchus numbers, 310954, and counts bracketings of ten terms together with a negative particle

The problem of counting parenthesizations was introduced to modern mathematics by Schröder (1870).

If this interpretation is correct it's a non-trivial combinatorial problem that Hipparchus solved. Hipparchus must have known some combinatorial techniques that are not in any contemporary sources that survive today but which were rediscovered in the 19th century.